Algebra, Advanced Math & Problem Solving

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Forty-four Math questions across four domains. Two of them — Algebra and Advanced Math — are about 70% of the section. That’s where your hours go.

Algebra (~35%)

• Linear equations and functions. Slope as rate of change. In word problems the slope is almost always the “per” quantity, and the y-intercept is the one-time or starting amount.
• Systems of equations. Substitution when one variable is already isolated; elimination when coefficients line up; Desmos when you just want the intersection.
• Inequalities. One rule to never forget: multiplying or dividing by a negative flips the sign.
• Number of solutions. Parallel lines (same slope, different intercepts) → no solution. Identical lines → infinitely many. This shows up as an abstract-coefficient question nearly every test.

Advanced Math (~35%)

• Quadratics. Know all three forms and what each hands you for free: standard ax² + bx + c gives the y-intercept, factored gives the roots, vertex gives the vertex. Sum of roots = −b/a; product = c/a.
• Exponential functions. Growth and decay. Distinguish a rate per period from a doubling or halving time — the distinction is the whole question in most exponential problems.
• Polynomials and rational expressions. Factoring, zeros, end behavior. If a value makes a denominator zero, it’s excluded.
• Function notation. f(g(x)) means work outward from the inside. Simple, and consistently mishandled under time pressure.

Problem Solving & Data Analysis (~15%)

• Ratios, rates, proportions, unit conversion. Set it up so the units cancel and the arithmetic follows.
• Percentages. Percent change = (new − old) / old. Successive percentages compound; they never add.
• Statistics. Mean, median, range, standard deviation as a concept — you’ll be asked to compare spread, never to compute it.
• Sampling and inference. Random sample → generalizable. Not random → not generalizable. That’s the entire tested idea.

Geometry & Trigonometry (~15%)

• Lines and angles. Parallel lines cut by a transversal; vertical, complementary, supplementary angles.
• Triangles. Similarity and congruence, the Pythagorean theorem, and the special right triangles (30-60-90, 45-45-90).
• Circles. Standard form (x − h)² + (y − k)² = r², plus arc length and sector area.
• Right-triangle trig. SOHCAHTOA, and the identity sin(x) = cos(90° − x).